A381018 a(n) is the number of primes in A000328 for r <= n.
1, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23
Offset: 1
Keywords
Links
- Thomas Ehrenborg, Gauss Circle Primes, arXiv:2502.06804 [math.GM], 2025. See Table 2 p. 4.
Programs
-
PARI
a(n) = sum(k=0, n, isprime(1 + 4*sum(j=0, k^2\4, k^2\(4*j+1) - k^2\(4*j+3))));
-
Python
from math import isqrt from sympy import isprime def A381018(n): return sum(1 for m in range(1,n+1) if isprime(1+(sum(isqrt(k*((m<<1)-k)) for k in range(1,m+1))<<2))) # Chai Wah Wu, Feb 13 2025
Comments